
import yfinance as yf
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline


# get data from yahoo finance 
data = yf.download("VUG BND XLV MCHI VT EWT VGLT IEMG VBK", period="max")["Close"]
data.dropna(inplace=True)
df = pd.concat([data], axis=1)
df.columns = ["VUG", "BND", "XLV", "MCHI", "VT", "EWT", "VGLT", "IEMG", "VBK"]

[*********************100%***********************]  9 of 9 completed


data.info()

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 2676 entries, 2012-10-24 to 2023-06-14
Data columns (total 9 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   BND     2676 non-null   float64
 1   EWT     2676 non-null   float64
 2   IEMG    2676 non-null   float64
 3   MCHI    2676 non-null   float64
 4   VBK     2676 non-null   float64
 5   VGLT    2676 non-null   float64
 6   VT      2676 non-null   float64
 7   VUG     2676 non-null   float64
 8   XLV     2676 non-null   float64
dtypes: float64(9)
memory usage: 209.1 KB


# plot historical data
for single_data in data:
    plt.figure(figsize=(8, 4), dpi=100)
    plt.plot(data[single_data], color="blue")
    plt.title(single_data)
    plt.xlabel("Time")
    plt.ylabel("Price")
    plt.grid(True)
    plt.show()


# log-returns of the assets
log_returns = np.log(df/df.shift(1))
log_returns.dropna(inplace=True)
log_returns.head(5)


log_returns.tail(5)


plt.figure(figsize=(10,6), dpi=100)
sns.heatmap(log_returns.corr(), cmap="Reds", linecolor="black", linewidth=0.1, annot=True);


np.random.seed(70)
n_portfolios = 10000
all_weights = np.zeros((n_portfolios, len(df.columns)))
ret_arr = np.zeros(n_portfolios)
vol_arr = np.zeros(n_portfolios)
sharpe_arr = np.zeros(n_portfolios)


# portfolios simulation(n_portoflios=10000)
for x in range(n_portfolios):
    weights = np.array(np.random.random(9))
    weights = weights / np.sum(weights)
    all_weights[x, :] = weights
    ret_arr[x] = np.sum((log_returns.mean() * weights * 252))
    vol_arr[x] = np.sqrt(np.dot(weights.T, np.dot(log_returns.cov() * 252, weights)))
    sharpe_arr[x] = ret_arr[x] / vol_arr[x]


print('Max sharpe ratio in the array is: {}'.format(sharpe_arr.max()))
print("It's located in the array: {}".format(sharpe_arr.argmax()))
reddot = (sharpe_arr.argmax())

max_sr_ret = ret_arr[sharpe_arr.argmax()]
max_sr_vol = vol_arr[sharpe_arr.argmax()]

print(all_weights[reddot, :])

Max sharpe ratio in the array is: 0.5845536385756669
It's located in the array: 9907
[0.09245677 0.05478004 0.00409467 0.00185034 0.00483573 0.27611547
 0.06868442 0.24107848 0.25610407]


import plotly.express as px


df = pd.DataFrame({'Volatility': vol_arr, 'Return': ret_arr, 'Sharpe Ratio': sharpe_arr.round(2)})
fig = px.scatter(df, x="Volatility", y="Return",
                 color='Sharpe Ratio',title = 'Efficient Frontier')
fig.show()

	VUG	BND	XLV	MCHI	VT	EWT	VGLT	IEMG	VBK
Date
2012-10-25	-0.001654	0.001571	0.006614	0.005814	0.003506	-0.005564	0.006277	0.000856	0.007937
2012-10-26	0.002126	-0.010257	-0.007237	-0.011888	-0.003271	0.011755	-0.003134	0.000570	-0.003960
2012-10-31	0.001651	0.000000	0.000830	0.000902	0.008159	0.007847	-0.001047	-0.000713	-0.007218
2012-11-01	-0.001533	0.012609	0.015839	0.029322	0.015549	-0.004570	0.014763	0.012611	0.008210
2012-11-02	0.000354	-0.010232	-0.009020	-0.004828	-0.017291	-0.005117	-0.010582	-0.009479	-0.005466

	VUG	BND	XLV	MCHI	VT	EWT	VGLT	IEMG	VBK
Date
2023-06-08	0.004964	0.001267	0.007128	0.011704	-0.000980	0.011467	0.006105	0.009864	0.006404
2023-06-09	-0.002065	0.004844	0.004252	-0.001318	-0.007469	-0.000792	0.001154	0.003070	0.003072
2023-06-12	0.002065	0.008993	0.002623	0.000000	0.010894	0.001900	0.006686	0.014262	0.003597
2023-06-13	-0.004411	0.014674	0.009228	0.013754	0.013804	-0.009536	0.007779	0.007037	0.005030
2023-06-14	0.000829	-0.002054	0.006766	0.015491	-0.006988	0.005891	0.001549	0.004796	-0.010315

Markowitz model and the efficient frontier¶

Info:¶

Correlation matrix¶

Plotting with ploty.express¶